Beyond the aesthetic reason of considering three Higgs doublets in analogy with three fermion families, or the intellectual challenge of attempting to reproduce the BGL structure with a larger scalar sector (see [1]} for an earlier attempt), there are other reasons to explore a 3HDM with similarly suppressed FCNCs. The BGL model is quite successful, but recent studies [2]} have found that its parameter space may be quite constrained. A possible criticism one may levy at the analysis of [2]} is that the latter has extended the BGL structure to the leptonic sector as well – something that is not mandatory as the model has enough freedom to
accommodate a flavour-preserving leptonic sector in what concerns the Yukawa interactions – which is what we will consider here. Nonetheless, this shows that even with natural FCNC coupling suppression via off-diagonal CKM matrix elements, the BGL structure can be quite constrained from experimental data. Working within the framework of
a 3HDM will in principle imply greater freedom in terms of parameters that can be adjusted to comply with experimental bounds.
